Polarized harmonic mappings and optimal moving frames

Autori

DOI:

https://doi.org/10.1478/AAPP.97S1A23

Parole chiave:

Dynamical systems, Lie group actions, foliations, moving frames, harmonic mappings

Abstract

We introduce the notion of a polarized harmonic mapping M → N of Riemannian manifolds and its infinitesimal analogue, a polarized harmonic connection. We study the integrability of these polarized harmonic connections when M is foliated by the action of a Lie group G.  In the case that M is a Kähler manifold and G has dimension 1, the polarized harmonic connection is integrable and we obtain a polarized harmonic mapping M → G, known as an optimal moving frame (or optimal G-frame). These ideas are illustrated using the dynamical system of N-point vortices in the plane.

Biografie autore

  • Serge Preston, Portland State University
    Department of Mathematics and Statistics, Portland, OR
  • Robert Thompson, Carleton College
    Department of Mathematics and Statistics, Northfield, MN

Dowloads

Pubblicato

2019-05-20

Fascicolo

Vol 97, SUPPL NO 1 (2019): Thermocon 2016

Sezione

THERMOCON 2016 (Conference Proceedings)

Licenza

Creative Commons License
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